%I #37 Apr 23 2024 20:33:31
%S 1,11,12,111,112,122,123,1111,1112,1122,1123,1222,1223,1233,1234,
%T 11111,11112,11122,11123,11222,11223,11233,11234,12222,12223,12233,
%U 12234,12333,12334,12344,12345,111111,111112,111122,111123,111222,111223
%N Numbers which are sum of distinct unary numbers (containing only ones), i.e., numbers which are sum of distinct numbers of the form (10^k - 1)/9.
%C Not the same as A096299, since a(1023) = 1234567900 which is not in lexicographic order. - _Ralf Stephan_, May 17 2007
%H David A. Corneth, <a href="/A110382/b110382.txt">Table of n, a(n) for n = 1..16383</a>
%F G.f.: 1/(1-x) * Sum_{k>=0} (10^(k+1) - 1)/9 * x^2^k/(1 + x^2^k). - _Ralf Stephan_, May 17 2007
%F a(n) = 10*a(floor(n/2)) + A000120(n) = Sum_{k=0..floor(log_2(n))} A000120(floor(n/(2^k)))*10^k. - _Mikhail Kurkov_, May 08 2019
%F a(n) = a(floor(n/2)) + A007088(n) = (10*A007088(n) - A000120(n))/9. - _Mikhail Kurkov_, Mar 03 2021
%t Nest[Append[#1, 10 #1[[Floor[#2/2] ]] + DigitCount[#2, 2, 1]] & @@ {#, Length[#] + 1} &, {1}, 36] (* _Michael De Vlieger_, Mar 12 2021 *)
%o (PARI) a(n) = sum(k=0, log(n)\log(2), hammingweight(n\(2^k))*10^k); \\ _Michel Marcus_, May 09 2019
%o (PARI) a(n) = my(b = Vecrev(binary(n))); sum(i = 1, #b, b[i] * 10^i-1) \ 9 + (vecmin(b) == 0) \\ _David A. Corneth_, May 19 2019
%Y Cf. A096299.
%K easy,nonn
%O 1,2
%A _Amarnath Murthy_, Jul 25 2005